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Topology optimization of continuum structures with local stress constraints. (English) Zbl 0924.73158
Summary: We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We first consider relevant stress criteria for porous composite materials, initially by studying the stress states of the so-called rank 2 layered materials. Then, on the basis of the theoretical study of the rank 2 microstructures, we propose an empirical model that extends the power penalized stiffness model. In the second part, solution aspects of topology problems are considered. To deal with the so-called ‘singularity’ phenomenon of stress constraints in topology design, we use an $$\varepsilon$$-constraint relaxation of the stress constraints. We describe the mathematical programming approach to solve the numerical optimization problems, and show results for a number of example applications.

##### MSC:
 74P99 Optimization problems in solid mechanics 65K10 Numerical optimization and variational techniques
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